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P R I N C I P L E S

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F O R M

A N D

W U C I U S

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D E S I G N

W O N G

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JOHN WlLEY & SONS, INC. New York

Chichester

Weinheim

Brisbane

0 F

Singapore Toronto

This book is printed on acid-free paper. Copyright O 1993 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permiss~on of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ@W~LEY.COM. This publication is designed to prov~deaccurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought.

Library of Congress Cataloging-in-PublicationData: Wong, Wucius. Principles of form and design / Wucius Wong. p. cm. Includes index. ISBN 0-471-28552-8 1. Computer-aided design. I. Title. TA345.W66 1993 745.4-dc20 Printed in the United States of America

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PREFACE

It was exactly two decades ago when my first book on design, Principles of TwoDimensional Design, was published. Subsequently, I wrote three more books: Principles of Three-Dimensional Design publ~shedin 1977, Principles of Color Design published in 1987, and Principles of TwoDimensional Form published in 1988. Each of these books was meant to be self-sufficient, but there is a common terminology and approach that links the separate texts. This prompted the publ~sherand I to look into the feasibility of a combined volume, including a general introduction, glossary, and index with appropriate cross references that would integrate these books. Because there is a limit to the physical size and weight of a book that can be conveniently handled by the reader and produced by the publisher, the present combined volume does not include the book Principles of Color Design. Its subject matter, dealing with color theories, makes it the best candidate to remain apart from the other books. As modest attempts at presenting a workable system of visual grammar, Principles of Two-DimensionalDesign, constituting Part 1 , lays down the basics with concentrationon flat, abstract forms; Principles of Two-Dimensional Form, constituting Part 2 , elaborates on the creation of forms with an emphasis on the representational aspects to extend one's visual vocabulary; and Principles of Three-Dimensional Design, constituting Part 3, examines the use of linear and planar materialsfor constructing freestanding objects in reality. In one single book the interrelationships among all three may become much clearer, since each tackles essentially the same design principles, but on different levels. The texts, diagrams, and illustrations of these earlier books are included here more or

less in their original form, only in a larger page format. All the key terms in the three books are explained in the newly written glossary which, with preceding notes, also serves as a handy reference to my particular version of visual grammar. The index, l~sting only the more important topics and frequently occurring terms, provides immediate access to various relevant parts of the texts. The new general introduction concentrates on computer methods and techniques to help readers who wish to avail themselves of the new technology. Whereas all the two-dimensional illustrations featured in the earlier books were the result of many hours of sketching and finishing work by my former students, now the same work can be done on a computer in only a fraction of the time. The development of computer hardware and software in recent years has already begun to effect a fundamental change in our ways of creating, teaching, and learning design. Becoming computer literate now seems a must for designers. In the preparation of this combined volume, my son, Benjamin, contr~butedmany of the diagrams and illustrations and designed the cover and various sectional pages. My wife, Pansy, helped with the general coordination of the materials and word-processing work. I am grateful for the generous support of the Aldus Corporation, which provided the graphics software programs Aldus Superpaint and Aldus FreeHand, with which all the new diagrams and illustrations were created, and also the Aldus Pagemaker program, which was used for the page layouts.

W.W. Englewood Cliffs, N.J.

CONTENTS

GENERAL INTRODUCTION Basic Computer Setup .......... 14 Graphics Programs ............... 15 Choosing a Program ............. 19 Starting to Draw ....................19 Creating a Shape ..................22 Achieving a Composite Shape ... ..........................................25 Establishing Repetition ......... 27 Establishing Radiation .......... 31 Establishing Gradation .........31 Establishing Similarity ...........33 Active and Visible Structures 35 Representational Forms ........36 Three-Dimensional Images ...36 Getting on with the Main Text .. 37

TWO-DIMENSIONAL DESIGN 1. INTRODUCTION What is Design ......................41 The Visual Language ............41 Interpreting the Visual Language ........................................ 41 Elements of Design ...............42 Conceptual Elements ............42 Visual Elements .....................42 Relational Elements ..............43 Practical Elements ................44 The Frame of Reference .......44 The Picture Plane ..................44 Form and Structure ...............44

2. FORM Form and the Conceptual Elements ........................... 45 Form as Point ........................45 Form as Line .........................45 Form as Plane .......................45 Form as Volume ....................47 Positive and [NegativeForms .. 47

Form and Color Distribution .... 47 The Interrelationships of Forms .. 49 Spatial Effects in Form lnterrelationsh~ps..............49 3. REPETITION Unit Forms .............................51

Repetition of Unit Forms ....... 51 Types of Repetition ............... 51 Variations in Repetition .........51 Subunit Forms and Superunit Forms ............................... 53 The Encounter of Four Circles ... 53 Repetition and Reflection ..... 54 Notes on the Exercises ......... 54

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4 STRUCTURE

Formal Structure ...................59 Semi-formal Structure ...........59 Informal Structure .................59 Inactive Structure ..................59 Active Structure ....................59 Invisible Structure .................61 Visible Structure ....................61 Repetition Structure ..............61 The Basic Grid ...................... 61 Variations of the Basic Grid .. 63 Multiple RepetitionStructures . . 63 Unit Forms and Structural Subdivisions .....................65 Repetition of Position ............65 Superimposition of Repetition Structures ......................... 66 Notes on the Exercises .............66

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5 SIMILARITY Similarity of Unit Forms ......... 69 Similarity of Shape ................ 69 Similarity and Gradation ....... 71 The Similarity Structure .........71 Notes on the Exercises .........71 6. GRADATION

Gradation of Unit Forms .......75 Planar Gradation ...................75

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Spatial Gradation ..................75 Shape Gradation ................... 77 The Path of Gradation ...........77 The Speed of Gradation .......77 Patterns of Gradation ............ 79 The Gradation Structure ....... 79 Alternate Gradation ............... 81 Relationship of Unit Forms and Structures in a Gradation Design ...................... ......... 82 Notes on the Exercises .............82 7. RADIATION Characteristics of a Radiation Pattern .............................. 87 The Radiation Structure ........87 The Centrifugal Structure ......87 The Concentric Structure ......88 The Centripetal Structure ...... 90 Superimposition of Radiation Structures ......................... 90 Rad~ationand Repetition ......90 Radiation and Gradation ......90 Structural Subdivisions and Unit Forms ........................93 Unit Forms in Radiation ........ 93 Oversize Unit Forms .............93 Irregular and Distorted Radiation .......................................... 94 Notes on the Exercises .............94

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10. CONCENTRATION

Concentration of Unit Forms in Formal Structures ........... 113 The ConcentrationStructure . . 114 Unit Forms in Concentration Structures .......................114 Notes on the Exercises ....... 117

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11 TEXTURE

Visual Texture .....................119 The Making of Visual Texture . . 119 Collage ................................121 Tactile Texture ....................122 Light and Color in Tactile Texture ........................................122 Notes on the Exercises ...........123

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12 SPACE

Positiveand Negative Space . . 127 Flat and Illusory Space ....... 127 Flat Forms in Illusory Space . . 127 Volume and Depth in Illusory .... 129 Space .................. .... Plane Representation in Illusory Space ..............................129 Fluctuating and Conflicting Space .......................... . .......... 131 Notes on the Exercises ...........13 1

TWO-DIMENSIONAL FORM

8 ANOMALY

Anomaly among Unit Forms ... 99 Anomaly within Structures .. 101 Notes on the Exercises ........... 10 1 9. CONTRAST

Contrast. Regularity. and Anomaly ........................................105 Contrast of Visual and Relational Elements .........................105 Contrast within a Form ........ 107 The Contrast Structure ........ 109 Dominance and Emphasis ... 109 Notes on the Exercises ...........111

1. ASPECTS OF FORM

Form .................................... 138 Three-Dimensional Form .... 138 Two-Dimensional Form ....... 139 Form and Shape ................. 139 Frame of Reference ............ 141 Form and Space ................. 141 The Visualization of Form ...... 142 Visualization with Lines ....... 143 Visualization with Planes ..... 143 Visualization with L~nesand 144 Planes .............................

Visualization with Points ......145 Visual~zationwith Texture ... 145 Types of Forms .................... 146 Representational Forms ...... 146 Natural Forms ......................147 Man-made Forms ................ 147 Verbal Forms ....................... 148 Abstract Forms .................... 148 Types of Shapes .................. 149 Calligraphic Shapes ........... 149 Organic Shapes ..................150 Geometric Shapes .............. 150

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2 DESIGNING A FORM Design and Form ................. 152 Singular Forms .................... 152

Plural Forms ........................ 153 Compound Forms ...............153 Unit Forms ........................ 154 Superunit Forms ..................154 Creating Geometric Shapes .. 155 Straight Lines ...................... 155 Circles .................................156 ..... ........ 156 Arcs .................. Relating Straight Lines ........ 157 Relating Circles ...................158 Relating Arcs ....................... 159 Relating Straight Lines. Circles. and Arcs ......................... 160 Angles and Pointed Tips .... 161 The Addition of Planes ........162 The Subtraction of Planes .. 163 The Interpenetrationof Planes .... ..................................... 163 The Multiplication of Planes .. 164 The Division of Planes ........165 Varying the Size of Planes .. 166 The Transformationof Planes .. 167 Folding Planes ....................168 Establishing Volume ........... 168 Regularity ............................ 169 Deviation .............................170 Symmetry ........................... 170 Asymmetry .......................... 171 Creating Organic Shapes ...... 172

C & S Curves ....................... 172 Shapes with Pointed Tips ... 173 Shapes with Rounded Tips ... 173 The Joining and Linking of Shapes ............................174 The Splitting. Tearing. and Breaking of Shapes ........ 174 Cutting and Removing Parts of Shapes ............................ 175 The Curl~ngand Twisting of Shapes ........................ .. 175 The Rippling and Creasing of Shapes ........................... 176 The Inflation and Deflation of Shapes ............................176 The Metamorphosis and Deformation of Shapes ... 177 The Proliferation of Shapes ... 177 Symmetrical Expression ..... 178 Variations of a Form ............179 Internal Variation .................179 External Variation ................180 Extension........................... 180 Superimposition ..................181 Transfiguration ....................181 Dislocation ..........................182 Distortion .............................182 Three-Dimensional Manipulation ..................... . . . . .. . ... 183 Further Developments ........ 184

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3 REPRESENTATIONAL FORMS Forms and Subjects ............. 186 Observing Natural Forms ... 186 Branching and Fanning ...... 187 Spirals and Undulations ..... 187 Affinity and Unity ................. 188 Observing Man-made Forms . . 188 Materials and the Assembly of Parts ................................189 Plans. Elevationsand Perspectives ......................... . . . ....... 189 Self-contained Compositions .... ........................................ 190 EstablishingSingular Forms .. 190

Establishing Plural Forms ... 192 Establishing Compound Forms ......................... ... 196 Compositions with Repetition ... .................... ..... .... . . .. 198 Two-way Continuance ........ 198 Four-way Continuance ........199 Six-way Continuance .......... 202 Development and Variations of the Repetition Structure ....203 Compositions with Radiation .... ...................................... 207 Full and Segmentary Radiation ..................... . . . ........ 207 Rotation and Translation .....208 Rotation and Reflection ...... 209 Rotation and Dilation ..........209 The Interception of Active Structural Lines ...............210 Compositions with Gradation .... ......................... .........212 Gradation of Shape .............212 Gradation of Size ................213 Gradation of Position .......... 213 Gradation of Direction ........214 Gradation of Proportion ...... 21 5 Compositions with Similarity .... ........................ ........ .216 Similarity and Repetition .....218 Similarity and Radiation ...... 218 Similarity and Gradation ..... 219 Compositions with Concentration ........................................219 Points of Concentration ......220 Linear Concentration .......... 221 Planar Concentration .......... 222 Compositions with Contrast ........ ........................................223 Contrast of Appearance .....223 Contrast of Placement ........ 226 Contrast of Quantity ............228 Compositions with Anomaly . . 230 Anomaly in Shape ...............230 Anomaly in Size ..................231 Anomaly in Color .................232

Anomaly in Texture .............232 Anomaly in Position and Direction 233 ........................................

THREE-DIMENSIONAL DESIGN 1. IN'TRODUCTION The Two-Dimensional World ..... ......................... .. 237 The Three-Dimensional World .. ........................................237 Two-Dimensional Design ....238 Three-Dimensional Design ...238 The Three Primary Directions . . 239 The Three Basic Views ....... 240 Elements of Three-Dimensional Design ............................241 Conceptual Elements ..........241 Visual Elements ...................242 Relational Elements ............244 Constructional Elements .....245 Form and Structure .............246 Unit Forms ...........................246 Repetition and Gradation ... 246

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2 SERIAL PLANES

Serial Planes ....................... 247 Dissection of a Cube ..........248 Positional Variations ............ 249 Directional Variations .......... 250 Construction Techniques .... 251

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3 WALL STRUCTURES

Cube. Column and Wall ...... 259 Spatial Cells and Unit Forms .. 260 Positional Variations of Unit 261 Forms .............................. Directional Variations of Unit Forms ............................. 262 Unit Forms as Distorted Planes .......................................263 Wall Structures Not Remaining Flat ..................................263

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Mod~ficationsof Spatial Cells ... ......................... . . ......... 264

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4 PRISMS AND CYLINDERS

The Basic Prism and Its Variations .................. ........ ......271 The Hollowed Prism ............272 Treatment of the Ends ........ 272 Treatment of the Edges ...... 273 Treatment of the Faces ....... 274 Joining of Prisms .................274 The Prism and the Cylinder .. 276 Variations of a Cylinder ....... 277 5. REPETITION

Repetition of Unit Forms ..... 284 Repetition Structure ............ 285 Arrangements of the Layers .. 286 Organization Within Each Layer ........................................ 286 Joining of Unit Forms ..........287 Square Prisms as Unit Forms or 288 Spatial Cells .................... L-Shape Unit Form or Spatial Cell .............................. ...... 288 Unit Forms in a Repetition Structure ......................... 289 6. POLYHEDRAL STRUCTURES The Platonic Solids ............. 295 The Archimedean Solids .... 297 Face Treatment ...................299 Edge Treatment .................. 299 Vertex Treatment ................. 300 Joining of Polyhedral Shapes . . 300 7. TRIANGULAR PLANES

Equilateral Triangles ........... 307 Isosceles Triangles .............308 Unequal-sided Triangles .... 309 The Octet System ...............309

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8 LINEAR FRAMEWORK

Construction with Planes ....315 Construction with Lines ......315

Joints ................ ..... .....316 Components for Linear Framework ........................317 Repetition of the Linear Framework ........................318 Stacking of Repeated Units ..319 Addition and Subtraction ....319 Interpenetration ...................320

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9 LINEAR LAYERS

Building up of Linear Layers ..324 Variations and Possibilities ...325 Gradation of Shape in Layer Construction ...................326

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10 INTERLINKING LINES

lnterlinking Lines on a Flat Plane ...............................333 Interlinking Lines in Space ....334 Materials and Construction ...336 Planar Construction for Interlinking Lines ............336 Interlinking Lines Within a Transparent Cube ..........337

GLOSSARY ......................... 345

GENERAL INTRODUCTION

Marks or shapes can happen spontaneously as we explore with tools, media, or substances for pictorial, textural, or sculptural effects and, in the process, decide on what is beautiful or exciting without consciously knowing how and why. We may pour in feelings and emotions during the process, resulting In a kind of artistic expression that reflects our personality in the form of our tastes and inclinations. This is the intuitive approach to visual creation. Alternatively, we can create having prior recognition of particular problems that must be dealt with. When we define the goals and the limits, analyze the situations, consider all available options, choose the elements for synthesis, and try to come up with the most appropriate solutions, this is the intellectual approach. It requires systematic thinking with a high degree of objectivity, although personal response to and judgment of beauty, harmony, and excitement must be present in all visual decisions. Obviously, in an attempt to sort out and articulate the principles, I have stressed the intellectual approach. Principles concern specific relationships and structures of elements, shapes, and forms. Some bias toward regularity may seem to prevail, for regularity of relationships and structures invariably has a mathematical basis and can be more precisely described. Regularity frequently becomes a point of departure, however, from which one can look into possibilities of partial or total transformation, modification, and deviation. To visualize any design of regularity using traditional tools and methods is often a laborious task. After sketching out the ideas, we use rulers and probably also compasses to construct shapes and structures, draw the outlines with a pen, and fill the open areas with a brush. This can take considerable time and

effort, and the result may not always be satwill suit a designer's particular requirements isfactory. If changes are necessary, the prpcess and how we can work with the computer to might have to be repeated again and again. pursue or implement the design principles Much of the work is mechanical and painslater elaborated in the main text. taking and it presents considerable frustrations for a beginner in design, who has to struggle Basic Computer Setup Computers corrle in different sizes and with with all the meticulous finishing techniques. varying capabilities and price tags. Generally, The advent of the computer has not only what a designer needs is a personal computer revolutionized our ways of information proof desktop size. Marly personal computers cessing, but also provided new methods for design creation. As the computer is primarily a belong to the IBM-compatible category and are simply referred to as PCs. They come in "number-crunching" machine, it is particularly numerous brands and models. The other suitable for,producing configurations of strict mathematicalorder. With the rapid development major category is the Macintosh, which is of many graphics software programs and re- made by only one manufacturer, and probably lated peripherals in recent years, the computer at a higher cost. What distinguishes the Macintosh is that it is the first computer to is now capable of accomplishing with great introduce graphical user interface. This efficiency most of the design work that is enables the designer to work directly with normally done with pencil, pen, and brush. Thus, it opens new horizons. pictorial elements with built-in commands Operating a computer today is relatively simple instead of merely typing verbal commands, and requires only a short period of training. The and to get printed results similar to what is displayed on screen. Because of this, computer, engineered with highly sophisticated technology, can be simply a new and powerful Macintoshes have the support of many tool to the designer, who does not really have rnore graphics software programs than the PCs. The gap between the Macintoshes to know how electronic signals work inside the and the PCs are narrowing, however, as circuitry to yield the on-screen image. What is fascinating is that, in simple computer oper- some Macintosh software programs are becoming available in PC versions. ations, a designer can produce with great At this moment, the Macintosh still repreexactitude many visual effects relating to principles of form and design and that trans- sents the choice of the design profession, and therefore it is this system on which my formations and changes are unbelievably discussion of computer techniques will coneasy to make. When done manually, without centrate. For working efficiently with most the computer, these same efforts would, of currently available software programs, a course, take many more renewed attempts computer for graphics purposes should have and hours to perform. a random-access memory (RAM) of no less We can well anticipate that the computer than 4 megabytes and an internal or external will soon become an indispensable tool in any hard drive with a memory exceeding 50 megadesigner's office or in design teaching studios of colleges and institutions. Our concern bytes. Other essential equipment includes a here is what basic equipment and software black-and-white Postscript laser printer, for

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a crisp output of the results on paper, and a scanner, which can be acquired at a later date, to deal with photographic and existing printed images. All computers are equipped with a central processing unit, a monitor, a keyboard, and a mouse. The central processing unit is the main component. It has an opening at the front to accept floppy disks, so that software programs recorded on such disks car1 be installed into the hard drive inside the unit or into a separate external drive. The monitor usually sits on top of the central processing unit, and its screen displays information and shapes in monochrome or in full color. The keyboard is similar to that of a typewriter, but it also includes keys that perform functions other than those of a typewriter. The mouse is a palm-size input device for moving a pointer on screen and has a button that can be depressed. When the pointer is in a desired location, the button of the stationery mouse can be "clicked" or it can be firmly held down while the mouse is "dragged." Cl~cking and dragging are the two basic mouse operations. A computer is practically useless without proper software. Software programs exist for many purposes, most commonly for wordprocessing or for producing spreadsheets, databases, or graphics. Word-processing programs are used for writing letters, articles, and books. Spreadsheet programs are used for accounting and financial work. Database programs are for storing and sorting information to produce reports, tables, and lists in a desirable order. Graphics programs are for creating pictorial images as artistic expression, as visual communication, as allover surface patterns, and for page layouts in desktop publishing work.

Graphics Programs Obviously, graphics programs are our main concern. In these, the screen takes the place of a piece of blank paper, with the mouse pointer assuming the role of a finger to move, point, and select, or that of a pen, pencil, or brush to create marks and shapes. On screen as a program is launched, a tool-boxappears, containing a range of tools. As we click with the mouse on one of the tools in the tool-box, the pointer becomes a cursor in a particular shape representing the selected tool and performs the function designated for the tool. On top of the screen is a menu bar from which we can access a number of pull-down menus by dragging the pointer. A menu is an onscreen display listing all available commands for editing and viewing as well as for special graphic effects beyond what is possible with the tools (Fig. 1). Each command may have submenus and may provide a dialog box for entering data or for selecting options. The screen is composed of a matrix of dots that are initially white in color. Some dots will appear in black, or sometimes in a chosen color, as you drag a tool cursor to make rnarks or shapes. Each dot stands for 1 4 File Edit Uiew O~Iions Draw Transform Font Text I

a picture elerrlent or pixel. There are normally 72 pixels to an inch, which is the standard screen resolution. Printing on a Postscript laser printer gives a much higher resolution to the shapes created. Resolution is measured in terms of number of dots per inch, or dpi. A laser printer can provide crisp outputs from 300 dpi to over two thousand. Postscript, a page description programming language developed by Adobe Systems to work with laser printer.^, helps to eliminate all ragged edges that might be visible on the screen. Moving the mouse pointer on screen locates a tool, clicking activates a command or selects an element, and dragging creates a line or shape. Mouse operation is also used in combination with depression of the shift, option and/or command keys on the keyboard. Although the keyboard is basically for typing with different fonts and sizes, it can be used for issuing short-cut commands and for entering numerical data to determine measurements and angles of the lines and shapes. It also contains a set of arrow keys for moving the mouse-pointer or selected elements up, down, left, or right. There are roughly six types of graphics

programs: paint, draw, page layout, image processing, font manipulation, and threedimensional modeling. A paint program enables us to "paint" intuitively on screen and produce bit-mapped images as strokes and shapes (Fig. 2). Bit-mapped images composed of pixels do not work with the Postscript language and tend to show some raggedness along any curved or diagonal edges. They are composed of densely packed independent square dots, representing the affected pixels, and can be magrrilied to facilitate editing with a pencil tool that adds new dots or removes existing ones (Fig. 3). Other tools particular to any paint program are the brush tool of different sizes and shapes for making lines or strokes of different widths and effects (Fig. 4) and a choice of patterns in the strokes (Fig. 5), a spraytool to sprinkle dots (Fig. 6), a fill tool to add color and pattern to an enclosed area or an unenclosed background (Fig. 7), an eraser tool to regain the original white color of the screen so that corrections can be made (Fig. 8). Each time as a line, stroke, or shape is formed on the screen, the new element fuses with all earlier ones it overlaps and becomes inseparable from them.

A draw program is for the creation of shapes as object-oriented images that are not bitmapped but are stored in the computer's memory as mathematical formulas defining the positions of anchoring points and paths. Although the screen display may appear very much the same as the bit-mapped images in a paint program, a selected object is indicated with open or sol~dblack dots along its outlines or at its four corners (Fig. 9). It can be enlarged unrestrictedlyand printed without the jaggedness that is associated with bit-mapped images (Fig. 10). Each shape or even each

component of a shape remains independent and can be separately selected at any time for alteration, transformation, or deletion. This allows the designer great flexibility in making subsequent changes. The tool-box features a special set of point tools for the construction of paths. Elements first appear on screen as thin black lines that can be changed into any weight, color, tone, or pattern (Fig. 11). Positioning is aided with rulers, guides, grids, and various commands. A page layout program imports text and graphics from a variety of files, effects 9 placement, sizing, scaling, and cropping of different page elements, and organizes pages in a sequential order. Text and illustrations flow from one page to the next and can be reshuffled, if desired. A master page can be used to determine the general layout and recurring elements for a whole section of pages. The program has word-processing I capabil~tiesfor changing font styles and sizes and for editing the text. Its graphics capabilities are limited to the adding of simple geometric elements, background color and shades, borders, and frames. I An image processing program allows scanning of images from photographs, sketches, or existing printed materials. It provides tools and commands for modification or transformation of the original images in the form of adjusting contrasts,tones, and colors; adding textures and patterns; retouching details; and introducing other special effects, as desired. Most of the tools and commands, however, can also be used on the blank screen for creation of bit-mapped images as in a paint program. A font manipulation program is for altering and custornizing existing fonts and may also be used to create new fonts. Some of these 11

programs have special transformation tools or commands for planar, spherical, or cylindrical distortions of typographical elements and imported graphic images. A three-dimensional modeling program combines plane and elevation views to establish forms of illusory volume and depth. The forrrls can be swiveled to show how they are seen from different angles, with a change of light source. Some programs may include animation capabilities.

Choosing a Program Every type of program just described is desirable, and ultimately it would be necessary to get all of them to meet different requirements. Most people tend to choose a paint program for their first attempt to create electronic pictures. A paint program IS by far the easiest to use and can also provide considerable fun. Simple paint programs produce only blackand-white images. The more sophisticated ones, however, enable you to tackle all colors of the spectrum - or a full range of grays if you work only with black-and-white outputs -and can simulate effects of actual painting and sketching on canvas or rough paper with dry or wet media. A paint program, however, is not designed for precision work. A paint composition contains shapes and brush strokes intermingled with one another in an almost irreversible process, although some programs may allow you to undo several times beyond the latest operation. Shapes and brush strokes are simply marks formed of loose pixels that are either affected or unaffected by the movement of a selected tool. Edges of the marks are not clear-cut boundaries. To work with most of the concepts and principles in this book, in which geometric elements, smooth

curves, sharp edges, and structures of strict regularity are often requ~red,a paint program is inadequate. For a modest start, all that may be needed is a good draw program. You can choose from several high-end draw programs on the market with similar features but distinctly different capabilities. My current choice is the Aldus FreeHand from Aldus Corporation, available in both Nlacintosh and PC versions, that facilitates working directly with shapes in their visual attributes, allows numerous levels of undoing, arranges elements in multiple layers, and provldes visible grids for accurate positioning, among other features. It is on this program that most of my explanations of computer techniques will be largely based. There IS the Aldus SuperPaint, also from Aldus Corporation, that the reader could consider as an alternative choice. Aldus SuperPaint combir~espaint and draw programs on interchangeable layers so that one can first create an image on the paint layer and immediately transfer it to the draw layer, or vice versa. The combination has definite advantages, particularly if you think you may want to do sorne painting work on screen. Many special effects are included on the paint layer for experimental work. Nevertheless, the drawing capabilities of Aldus SuperPaint are certainly not as extensive as those of the Aldus FreeHand.

Starting to Draw With an appropriate draw program properly installed 11-1the hard disk drive, the program can be launched. On screen, the menu bar and the tool-box appear. Opening a new file causes a vertically oriented rectangular frame to appear in the center of the screen.

tool plots points between straight and curved paths to ensure a smooth linear flow without noticeable bumps (Fig. 15). Plotting a point is accomplished by clicking with a tool cursor. The pen tool combines the function of the corner tool and the curve tool. It plots points to make straight lines with clicking and makes curved lines as you drag the mouse (Fig. 16). Other tools include a rectangle tool for drawing squares and rectangles (Fig. 1 7 ) , a rounded-rectangle tool for drawing roundedcorner squares and rectangles (Fig. 18), 12

This IS the fit-~n-windowvlew, showlng the entire page reduced (Flg. 12). A command from the v~ewmenu on the menu bar changes thls to a 100% vlew or a vlew of deslrable mag n~ficationlreduct~on Activating a preview command from this view menu enables you to work not just In key-line mode but dlrectly with lines and shapes showlng all intended attributes. The view menu also allows the dlsplay of rulers wlth appropriate markings, palette boxes for attribution of colors, line welghts and control of layers, and an information bar contalnlng measurernents and angles of the elements, and vert~callhor~zontal 13 positions of the polnter. Furthermore, there an ellipse tool for drawing circles and elllpses are guldes In dotted or colored llnes that (Fig. 19),a llne tool for drawing straight can be dragged from the rulers, and a grrd lines (Fig. 20), and a freehand tool for In a matrix of equ~d~stant dots established drawing irregular curves (Fig. 21). All these wlth the document setup command In the tools effect shapes when the mouse is file menu. dragged. More than half of the tools In the tool-box are In addition, there is the type tool for origifor originat~ngshapes. The point tools Include nating characters on the keyboard, which a corner tool, a curve tool, a connector tool, can be transformed into the desirable size and a pen tool. The corner tool plots points and font style for use as shapes in a design. to make straight paths and sharp bends Pictorial fonts such as the Zapf Dingbats, (Fig. 13). The curve tool plots points to make consisting of symbols and naturalistic shapes, winding curved lines (Flg. 14). The connector are also a handy choice for the designer

Creating a Shape Points mark the beginning and end of a path and can occur along any part of the path. An open path is one that has disconnected end points. Connecting end points establishes a closed path. The rectangle or ellipse tool produces a closed path right away. Any shape is constructed of points and paths. Points define key positions of a path. The path must take on attributes to be visible. This is accompl~shedwith the fill and line command in the attributes menu, which provides a dialog box for separately Caps and joins can also be specified for any open path. Caps, which may be square or round, are added to the endings of lines (Fig. 25). Joins occur where two lines meet at an angle, and they can be in a miter, round, or beveled shape (Fig. 26). Moreover, the line can be continuous or dashed (Fig. 27) and car1 be patterned (Fig. 28). A closed path allows the covering of a plane with a flat fill, a graduatedfill, a radial fill, or a patterned fill that could be in a gray tone or color (Fig. 29). As the closed path is filled, line attributes should be chosen in entering fill and line data. An open path takes the shape of a line with attributes that include weight, color, and pattern. The weight of a line can be so thin as to be barely visible and as thick as two inches (Fig. 23). The color of a line can be in any gray ranging from 10% to 80% black (Fig. 24), plus solid black, white, and none, if you do not work in full color. White and none may appear the same on screen, but white refers to an opaque element that can hide anything beneath it; whereas none is transparent and invisible.

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order to obtain an outlined shape (Fig. 30). If you do not want an outline, you can just enter none for the l~neattributes in the dialog box. Paths can be edited before or after the attributes.Any point on a path can be specially selected and moved with the arrow tool pointer and can be dragged to any desirable new location to effect change in the path. There are three types of points, the corner point, the curve point, and the connector point, normally resulting from the use of those respective tools. One type of point can be substituted for another, using the points

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command in the element menu. In this way, an angular path can become smooth, or a smooth path can become angular (Fig. 31). There are two nonprinting control handles associated with every curve point. They are displayed on screen when the curve point is selected. Dragging each handle with the arrow pointer adjusts the convexity or concavity of a curved path (Fig. 32). A point can be added to the path with any appropriate point tool to facilitate manipulation or removed with the points command. Point removal can change a shape significantly. Holding down the shifi key on the keyboard 7 as you drag with the rectangle tool produces a perfect square, and the ellipse tool a perfect circle. Rectangles, squares, ellipses, and circles all come with four handles, and without ungrouping you can drag any handle to resize and reshape the path without irregular distortion (Fig. 33). With activation of the ungroup command in the element menu, the handles change into points and each point can be dragged freely to change the shape (Fig. 34). The tool-box also contains tools for effecting changes in existing shapes. The rotating tool is for making directional changes (Fig.

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35). The reflecting tool is for fl~ppingthe shape to obtain its mirrored image (Fig. 36). The scaling tool is for resizing and reproportioning (Fig. 37). The skewing tool is for slanting a shape upward, downward, or sideways (Fig. 38). The magnifying tool is for blowing up any portion of the shape to help with critical modifications. The tracing tool is to perform automatic tracing of the outlines of any shape (Fig. 39). The knife tool is for cutting and splitting a path.

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Achieving a Composite Shape A composite shape consists of two or more shapes in a process involving addition, subtraction, multiplication, or even division. Addition is the overlapping of two or more shapes that can remain separately discernible with conspicuous line attributes or different fills (Fig. 40) or fuse together with the same fill but no line attributes (Fig. 41). Subtraction is the effect of placing an opaque white shape, which functions as a negative shape, in front of a filled shape (Fig. 42). Multiplication is creating the same shape more than once, by using the copy and paste commands, the clone command, or the duplicate command,

all in the edit menu (Fig. 43). Each copy of the shape can be moved with the arrow pointer or any of the arrow keys on the keyboard to attain the desirable configuration.You can have as many copies as desirable, and each copy can be separately moved, rotated, and reflected. Division requires a more complicated procedure. This is possible with an ungrouped closed path, such as a rectangle or ellipse, on which you can engage the knife tool to insert breaking points. Afterwards, each segment or pair of segments is moved away from the path with the arrow pointer. Then the join

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command in the same menu is used to join points of separate segments with straight lines. The process rnust be repeated to obtain a number of divisions. Individual shapes resulting from division can be shifted and rotated to establish a new corlfiguratiorl (Fig. 44). Overlapping shapes can interpenetrate one another, with the overlapped area or areas showing the white of the screen. This is achieved by activating the join command as the shapes are selected and ungrouped (Fig. 45). All the above methods car1 be cornbir~ed to achieve a composite shape (Fig. 46). 47

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Establishing Repetition As just discussed, a shape in repetition can be used to create a composite shape. Any shape can become a unit form for repetition in a composition (Fig. 47). A group of connected or disconnected shapes can also be used as superunit forms for repetition (Fig 48). If a shape or a group of shapes is copied by the computer, it stores the entire configuration in a clipboard file and can repeatedly paste the configuration at locations indicated by the arrow pointer on screen to attain an informal composition. Activating the clone command places a copy of the shape directly on top of the original. The copy remains unnoticeable until it is moved with the arrow pointer or the arrow keys. If necessary, the dialog box associated with the move command can be accessed in order to enter numerical descriptions for a precise vertical/horizontal move. After the copy is moved once, activating the duplicate command will cause subsequent copies to appear with identical moves. All such moves can form a row or column, which can again be cloned, moved, and duplicated to spread the repetition vertically, horizontally,

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Establishina Radiation Any element-or shape lns~dea repetltlon structure may be ~nd~vldually rotated w ~ l h the rotatlng tooi Systemat~crotatlor1 of the unlt forrns properly arranged can glve a cornpos~t~on the effect of radiabon (Fig 61) Flrst, the ~nformat~on bar may be d~splayed to show the deslrabe degrees of rotaton and then for preclson corltro the data shown can be entered n a dalog box provided by the rotat~ngtool Before rotating a serles of shapes I ~ regular I Intervals, the shape must be cloned Upon rotatlng the unrotated orlglnal and the rotated copy are brought next to each other Then the duplicate command IS used to obtain all necessary further rotated coples to compete the serles (Fg 62) The crucal thng here IS the placement of the center of rotallon, whlch can affect the cornposltlor s~gn~fcantly (Rg 63) Elements can be rotated to create a radatlng corrposlte shape to be used as a superunll form or to establ~sha formal composlllon show~ngan underyng radiation structure A radat~onstructure template can be des~gned by rotatlng hnes regularly In a full revolut~on, w~lhthe~rconvergence or lntersectlon mark~ng

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the center, and superimposing on these a seres of concentric circles (Fig. 64). With the completed rad~ationstructure locked and transferred to the background layer, arrangement of u n t forms can revolve around the same center with the same angle of rotation as the structural lhnes (Fig. 65). If you do not use a structure template, ~ O L I can directly clone and rotate a shape with subsequent duplications. The result is sometimes unpredictable and the rotation may have to be redone over and over to achieve desirable effects.

Establishing Gradation The elernent menu provides a blend command that produces gradation almost instantar~eously. To effect a blend, you must first select two shapes defining the beginning and the end of the blend. Each shape must be first ungrouped so that one of the points on ils path can be selected to constrain the blend. A dialog box appears as the command is activated and in this can be entered the number of steps, which can range from one to hundreds. Not only shapes can be blended, but also line weights and colors. After bierld~ng,the series

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of shapes appear as a group, but you can hold down the option key as you use the arrow pointer to subselect a shape at the beginning or end of the blend and make necessary changes (Figs. 6 M 8 ) . Any change will affect the entire series of blended shapes. The entire series can be further transformed (Fig. 69) and can also be ungrouped in order to effect change in individual shapes within the series (Fig. 70). Blending places intermediate shapes equidistantly, providing a range of unit forms in gradation that can subsequently be repeated or reblended to achieve a composition with an underlying repetition structure (Fig. 71). Blending two parallel lines of the same weight but different grays in many steps can result in a very smooth tonal gradation of a plane (Fig. 72). Blending two linear shapes of different directions can establish the effect of radiation (Fig. 73). The blend command does not, however, provide for instantly erecting a gradation structure. This must be independently constructed with guides or lines made with an appropriate tool. With a gradation structure as a background template, you can then use the blend command to create a series of unit forms in tonal, shape, or other kinds of gradation for manual positioning (Fig. 74).

Establishing Similarity In a composition containing repeated shapes in a formal structure, random variations of size, direction, and general attributes can be created to achieve the effect of similarity (Fig. 7577), or individual shapes can be freely manipulated to attain shape changes (Fig. 78). You can also use the blend command to produce a series of gradually changing shapes for rearrangement in a nonsequential order to accomplish the effect of similarity (Fig. 79).

The existence of an underlying similarity structure can be implied if the arrangement of shapes in a repetition structure is deliberately inconsistent inside particular structural subdivisions (Fig. 80). A similarity structure can be constructed with the line tool or any point tool, but it is not worth the trouble unless the structure is active or visible. Active and Visible Structures Structural lines,dividethe picture area into subdivisions. In an inactive structure, shapes and their surrounding space flow uninterruptedly

between subdivisions. In an active structure, each subdivision is an independent spatial cellwith the background assuming the status of a shape with desirable attributes. Shapes and cells can alternate as positive and negative elements (Fig. 81), or they can have different attributes (Fig. 82). If the background has a fill of opaque white, shapes in adjacent cells intruding into it can be blocked at its borders (Fig. 83). Converting the background shape of the cell into an attributable shape can be done by tracing its bordering outlines with an appropriate tool to form a closed

path and sending it behind the unit form with the send backward or send to back command in the element menu. This background shape and the associated unit form can be seen as a composite shape. Giving line attributes to the background shape, which may or may not have a fill, produces a visible structure. Structural lines thus become lattice-like elements working with the unit forms (Fig. 84). Representational Forms Shapes obtained with the type tool, using a pictorial font, can be representational forms. After their conversion to paths, they can have line and fill attributes, and can be transformed and repeated to establish a composition (Fig. 85). A shape can also be traced with the tracing tool, but automatic tracing of complex shapes may not always produce satisfactory results. Connecting a scanner to the computer, you can import a photographic or printed image that can be manipulated and repeated (Fig. 86) or used as a template on which you can trace with the tracing tool or redraw with the freehand or pen tools. After being traced or redrawn, the shape can be given any desirable line and fill attributes and can be used with or without transformation as a unit form in a composition (Fig. 87). Three-Dimensional Images A drawing program is not specifically intended for creation of three-dimensional images. Blending of simple shapes that overlap in a row, however, can establish an illusion of a three-dimensional form composed of serial planes (Fig. 88). Also, a simple linear framework that gives a three-dimensional illusion can be created with the pen tool or any other

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appropriate tool (Figs. 89, 90). In most cases, a three-dimensional form that looks good in one particular two-dimensional view can be very ordinary or even disappointing in real life and may be impossible for construction with physical materials when elements must be solidly joined or supported. Exercises in three-dimensional design should be accomplished with actual models. Computer-aided design is only for the advanced user who relies on the computer mainly for expediting production of planes and elevations and for perspective presentations. Getting on with the Main Text Full explanations of some of the design terms and concepts are in the main text. Descriptions of computer techniques here may not be complete, and can never be totally adequate. Thus, the reader will need to refer to special manuals for the computer and its peripherals, as well as to the user manual and guide books for any chosen software program. Software programs get updated frequently, with improved conveniences and added features, and hardware can become easily antiquated when newer models with increased power appear on the market. This general introduction is intended only to help the reader see the essential link between the. language of visual form and computer language. Then the challenge becomes getting on with the effort to tackle all the concepts, principles, and exercises in form and design with growing computer literacy, increasing aesthetic sensitivity and technical competence

1'

e m ~ l o va line that is visible to re~resenta line that is conceptual. The visibie line not only has length but also breadth. Its color and texture are determined by the materials we use and the way we use them. Thus, when conceptual elements become vlslble, they have shape, size, color, and texture. Visual elements form the most prominent part of a design because they are what we can actually see. n g can be seen (a) Shape - ~ n ~ t h i that has a shape which provides the main identification in our perception. (Fig. 2a) (b) Size - All shapes have size. Size is relative if we describe it in terms of bigness and smallness, but it is also physically measurable (Fig 2b) (c) Color - A shape IS dlstlngu~shed from ~ t ssurround~ngsbecause of color Color here is used ~nits broad sense, comprlsing not only all the hues of the spectrum but also the neutrals (black, white, and all the Intermediate grays), and also all their tonal and chromatic variations. (Fig. 2c) (d) Texture - Texture refers to the surface characteristics of a shape. This may be plain or decorated, smooth or rough, and may appeal to the sense of touch as much as to sight. (Fig. 2d) 8

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Relational Elements This group of elements governs the placement and interrelationship of the shapes in a design. Some are to be perceived, such as direction and position; some are to be felt, such as sDace and aravitv. (a) ~ i r e c t i d n- Direction i f a shape depends on how it is related to the observer, to the frame that contains it, or to other shapes nearby. (Fig. 3a) (b) Position - The position of a shape is u

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judged by its relationship to the frame or the structure (see Chapter 4) of the design. (Fig. 3b) (c) Space - Shapes of any size, however small, occupy space. Thus, space can be occupied or left blank. It can also be flat or illusory to suggest depth. (Fig. 3c) (d) Gravity - The sense of gravity is not visual but psychological. As we are pulled by the gravity of the earth, we tend to attribute heaviness or lightness, stability or instability to indi.vidual shapes or groups of shapes. (Fig. 3d)

Practical Elements The practical elements underlie the content and extension of a design. They are beyond the scope of this book, but I would like to mention them here: (a) Representation - When a shape is derived from nature or the man-made world, it is representational. Representation may be realistic, stylized, or near-abstract. (b) Meaning - Meaning is present when the design conveys a message. (c) Function - Function is present when a design is to serve a purpose. The Frame of Reference All the above elements normally exist within a boundary which we call a "frame of reference." The frame of reference marks the outer limits of a design and defines an area within which the created elements and left-over blank space, if any, all work together. The frame of reference is not necessarily an actual frame. If it is, then the frame should be considered as an integral part of the design. The visual elements of the visible frame should not be overlooked. If there is no actual frame, the edges of a poster, the page of a magazine, the various surfaces

of a package all become frames of reference for the respective designs. The fral-ne of reference of a design can be of any shape, though it is usually rec.tangular. The die-cut shape of a printed sheet is the frame of reference of the design that is contained in it.

The Picture Plane Within the frame of reference lies the picture plane. The picture plane is actually the plane surface of the paper (or any other material) upon which the design is created. Shapes are directly painted or printed on this picture plane, but they may appear to be above, below, or unparallel to it because of spatial illusions, which will be fully discussed in Chapter 12. Form and Structure All the visual elements constitute what we generally call "forrn," which is the primary concern in our present enquiry into the visual language. Form in this sense is not just a shape that is seen, but a shape of definite size, color, and texture. The way form IS created, constructed, or organized along with other forms is often governed by a certain discipline which we call "structure." Structure which involves the relational elemer~tsis also essential in our studies. Both forrn and structure will be thoroughly discussed in the chapters to follow.

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A line generally conveys the feeling of thinness. Thinness, like smallness, is relative. The extreme ratio between length and breadth of a shape makes it a line, but there is no absolute criterion for this. Three separate aspects should be considered in a line: Form and the Conceptual Elements The overall shape - This refers to its generAs already pointed out, the conceptual eleal appearance, which is described as straight, ments are not visible. Thus point, line, or curved, bent, irregular, or hand-drawn. (Fig. 6a) plane, when visible, becomes form. A point The body - As a line has breadth, its on paper, however small, must have shape, body is contained within two edges. The size, color, and texture if it is meant to be shapes of these two edges and the relationseen. So must a line or a plane. Volume reship between them determine the shape of mains illusory in two-dimensional design. Visible points, I~nes,or planes are forms in the' body. Usually the two edges are smooth and parallel, but sometimes they may cause the true sense, although forms as points or the body of the line to appear tapering, knotlines are still simply called points or lines in common practice. ty, wavy, or irregular. (Fig. 6b) The extremities - These may be negligible when the line is very thin. But if the line is Form as Point A form is recognized as a point because it is quite broad, the shapes of its extremities may small. become prominent. They may be square, round, pointed, or any simple shape. (Fig. 6c) Smallness, of course, is relative. A form may appear fairly large when it is confined Points arranged in a row may evoke the in a tiny frame of reference, but the same form feeling of a line. But in this case the line is may appear rather small when it is put inside a conceptual and not visual, for what we see is much greater frame of reference. (Fig. 4) still a series of points. (Fig. 6d) The most common shape of a point is that of a circle which is simple, compact, nonForm as Plane angular, and non-directional. However, a On a two-dimensional surface, all flat forms point may be square, triangular, oval, or that are not commonly recognized as points even of a somewhat irregular shape. (Fig. 5) or lines are forms as plane. Thus the main characteristics of a point are: A planar form is bound by conceptual lines (a) its size should be comparatively small, which constitute the edges of the form. The and characteristics of these conceptual lines and (b) its shape should be rather simple. their interrelationships determine the shape of the planar form. Form as Line Planar forms have a variety of shapes, A form IS recognized as a line because of which may be classified as follows: two reasons: (a) its breadth is extremely (a) Geometric - constructed mathematinarrow, and (b) its length is quite prominent. cally. (Fig. 7a)

CHAPTER 2: FORM

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(b) Organic - bounded by free curves, suggesting fluidity and growth. (Fig. 7b) (c) Rectilinear - bound by straight lines which are not related to one another mathematically. (Fig.7c) (d) Irregular - bound by straight and curved lines which are not related to one another mathematically. (Fig. 7d) (e) Hand-drawn - calligraphic or created with the unaided hand. (Fig. 7e) (f) Accidental - determined by the effect of special processes or materials, or obtained accidentally. (Fig. 7f) Planar forms may be suggested by means of outlining. In this case the thickness of the lines used should be considered. Points arranged in a row can also outline a planar form. Points or lines densely and regularly grouped together can also suggest planar forms.They become the texture of the plane.

Form as Volume Form as volume is completely illusory and demands a special spatial situation. A full discussion of this will be found in Chapter 12.

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Positive and Negative Forms Form is generally seen as occupying space, but it can also be seen as blank space surrounded by occupied space. When it is perceived as occupying space, we call it "positive" form. When it is perceived as blank space surrounded by occupied space, we call it "negative" form. (Fig. 8) In black-and-white design, we tend to regard black as occupied and white as unoccupied. Thus, a black form is recognized as positive and a white form as negative. But such attributions are not always true. Especially when forms interpenetrate or intersect one another (see the section on the inter-

relationships of forms later in this chapter), what is positive and what is negative are no longer easily distinguishable. Form, whether positive or negative, is commonly referred to as the "figure," which is on a "ground." Here "ground" denotes the area surrounding the form or the "figure." In ambiguous cases, the figure-ground relationship may be reversible. This will be discussed in Chapter 12.

Form and Color Distribution Without changing any of the elements in a design, the distribution of colors within a definite color scheme can have a large range of variations. Let us have a very simple example. Suppose we have a form which exists within a frame, and we can only use black and white. Four different ways of color distribution can be obtained: (a) white form on white ground (Fig. 9a) (b) white form on black ground (Fig. 9b) (c) black form on white ground (Fig. 9c) (d) black form on black ground (Fig. 9d) In (a), the design is all white, and the form disappears. In (b), we have a negative form. In (c), we have a positive form. In (d), the design is all black, and the form disappears in the same way as in (a). Of course, we can have the form outlined in black in (a), and outlined in white in (d). (Fig. 10) If the design increases in complexity, the different possibilities for color distribution will also be increased. To illustrate once again, we have two circles crossing over each other within a frame. In the previous example, we have only two defined areas where we can distribute our colors. Now we have four areas. Still using black and white, we can present sixteen distinct variations instead of only four. (Fig. 11)

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The lnterrelationships of Forms Forms can encounter one another in numerous ways. We have just demonstrated that when one form crosses over another, the results are not as simple as we may have thought. We now again take two circles and see how they can be brought together. We choose two circles of the same size to avoid unnecessary complication. Eight different ways of interrelationship can be distinguished: (a) Detachment - The two forms remain separate from each other although they may be very close together. (Fig. 12a) (b) Touching - If we move the two forms closer, they begin to touch. The continuous space which keeps the two forms apart in (a) is thus broken. (Fig. 12b) (c) Overlapping - If we move the two forms still closer, one crosses over the other and appears to remain above, covering a portion of the form that appears to be underneath. (Fig. 12c) (d) Interpenetration - Same as (c), but both forms appear transparent. There is no obvious above-and-below relationship between them, and the contours of both forms remain entirely visible. (Fig. 12d) (e) Union - Same as (c), but the two forms are joined together and become a new, bigger form. Both forms lose one part of their contours when they are in union. (Fig. 12e) (f) Subtraction - When an invisible form crosses over a visible form, the result is subtraction.The portion of the visible form that is covered up by the invisible form becomes invisible also. Subtraction may be regarded as the overlapping of a negative form on a Positive form. (Fig. 12f) (g) Intersection - Same as (d), but only the portion where the two forms cross over each other is visible. A new, smaller form

emerges as a result of intersection. It may not remind us of the original forms from which it is created. (Fig. 12g) (h) Coinciding - If we move the two forms still closer, they coincide. The two circles become one. (Fig. 12h) The various kinds of interrelationships should always be explored when forms are organized in a design.

Spatial Effects in Form lnterrelationships Detachment,touching, overlapping, interpenetration, union, subtraction, intersection, or coinciding of forms - each kind of interrelationship produces different spatial effects. In detachment, both forms may appear equidistant from the eye, or one closer, one farther away. In touching, the spatial situation of the two forms is also flexible as in detachment. Color plays an important role in determining the spatial situation. In overlapping, it is obvious that one form is in front of or above the other. In interpenetration, the spatial situation is a bit vague, but it is possible to bring one form above the other by manipulating the colors. In union, usually the forms appear equidistant from the eye because they become one new form. In subtraction, as well as in interpenetration, we are confronted with one new form. No spatial variation is possible. In coinciding, we have only one form if the two forms are identical in shape, size, and direction. If one is smaller in size or different in shape and/or direction from the other, there will not be any real coinciding, and overlapping, interpenetration, union, subtraction, or intersection would occur, with the possible spatial effects just mentioned.

CHAPTER 3: REPETITION

Unit Forms When a design I S composed of a number of forms, those that are of identical or sirnilar shapes are "unit forms" which appear more than once in the des~gn. The presence of ur~iiforrns helps to unify the design. Unit forms can be easily discovered in most designs if we search for them. A design may contain more than just one set of wnlt forms. Unlt forms should be simple. Overly compl~catedunit forms often tend to stand out too much as rndivid~jalforms, and the effect of un~tymay be destroyed. 1

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"epetition of Unit Forms II we Ltse the same form more than once in a deslgn, we use it in repetition. Repetition is the s~mplestmethod in designing. Columns and windows in architecture, the legs of a piece of furniture, the pattern on fabrics,tiles on the floor are obvious examples of repetition. Repetition of unit forms usually conveys an immediate sense of harmony. Each repetilive unit form is like the beat of some kind of rhythm. When the unit forms are used in larger size and smaller numbers, the design may appear simple and bold; when they are Infinitelysmall and in countless numbers, the design may appear to be a piece of uniform texture, composed of tiny elements.

14

Types of Repetition In precise thinking, repetition should be

cor~sideredin respect of each of the visual and relational elements: (a) Repetition of shape - Shape is always the most irnportant element. Repetitive shapes can have different sizes, colors, etc. (Fig. 13a) (b) Repetition of size - Repetition of size is possible only when the shapes are also repetitive or very similar. (Fig. 13b) (c) Repetition of color - This means that all the forms are of the same color but their shapes and sizes may vary. (Fig. 13c) (d) Repetition of texture - All forms car1 be of the same texture but they may be of different shapes, sizes, or colors. In printing, all solidly printed forms with the same type of ink on the same surface are regarded as having the same texture. (Fig. 13d) (e) Repetition of direction - This is possible only when the forms show a definite sense of direction without the slightest arnbigui-ty. (Fig. 13e) (f) Repetition of position - This has to do with how forms are arranged in connection with the structure which will be discussed in the next chapter. (g) Repetition of space - All forms can occupy space in the sarne manner. In other words, they may be all positive, or all negative, or related to the picture plane in the same way. (h) Repetition of gravity - Gravity is too abstract an element to be used repetitively. I t is dil'ficult to say that forrns are of equal heaviness or Ilghtness, stability or instability, unless all other elements are in strict repetition.

Variations in Repetition Repetition of all the elements may seem monotonous. Repetition of one element alone may not provoke-fhe sense of order and

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harmony which we normally associate with the repetition discipline. I f rnost of the visual elements are in repetition, possibilities in directional and spatial variations should be explored. Directional variations - With the exception of the plain c~rcle,all forms can vary in direction to some extent. Even circles can be grouped to give a sense of direction. Several kinds of directional arrangements can be distinguished: (a) repeated directions (Fig. 14a) (b) indefinite directions (Fig. 14b) (c) alternate directions (Fig. 14c) (d) gradational direct~ons(Fig. 146) (e) similar directions (Fig. 14e) Repeated and the more regularly arranged directions can be mingled with some irregular directions. Spatial variations - These can be obtairred by having the forms encounter one another in a multiple of interrelationships as described in the previous chapter. Irnaginatlve use of overlapping, interpenetration, union, or positive and negative cornbinations can lead to surprising results.

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Subunit forms and Superunit forms A unit form can be composed of smaller elements that are used in repetition. Such smaller elements are called "subunit forms." If the unit forms, in the process of being organized in a design, are grouped together to become a bigger form which is then used in repetition,we call these new, bigger forrns "superunit forrns." Superunit forms can be used along with regular unit forms in a design if necessary. Just as we can have more than one single type of unit form, we can have a variety of superunit forms if so desired.

The Encounter of Four Circles To illustrate the formation of superunit forms, we will now see how four circles of the same size can be grouped together. The possibill~l:iesare definitely unlirnited, but we can examine some of the common ways of arrangement as follows: (a) Linear arrangement - The circles are lined up as guided by a conceptual line which passes through the centers of all the circles. The conceptual line rnay be straight, curved, or bent. The distance between the circles may be regulated as desired. Note, in an extreme case, that each of the circles crosses over all the other three simultaneously, producing as many as thirteen distinct divisions. (Fig. 15a) (b) Square or rectangular arrangement - In this case the four circles occupy four poir~tswhich, when joined together, can form a square or a rectangle. As in (a), an extreme case also shows thirteen divisions when all the circles deeply interpenetrate one another. (Fig. 15b) (c) Rhombic arrangement - Here the four circles occupy four points which, when joined together, can form a rhombus. Regulating the distance between the circles, various types of superunit forms can emerge. (Fig. 15c) (d) Triangular arrangement - Here the four circles are arranged so that three occupy the three points of a triangle, with the fourth in the center. This also prodl~cesinteresting superunit forms. (Fig. 15d) (e) Circular arrangement - Four circles in circular arrangement turn out the same result as in square arrangement, but circular arrangement can be very unique with more circles. Four circles can be arranged to suggest the arc of a circle, but this may be similar to a lir~eararrangement. (Fig. 15e)

Repetition and Reflection Reflection is a special case of repetition. By reflection we mean that a form is mirrored, resulting in a new form which looks very much like the original form, except that one is left-handed, and the other is right-handed, and the two can never exactly coincide. Reflection is only possible when the form is not symmetrical, because a symmetrical form turns out to be the same form in reflection. Rotation of a form in any direction can never produce its reflected form. The reflected form has a completely different set of rotations. (Fig. 16) All symmetrical forms can be divided into two parts: one component form and its reflection. The union of these two parts produces the symmetrical form. Notes on the Exercises Figures 17a, b, c, d, e, and f all represent the results of one simple problem: repetition of unit forms (circles) of the same shape and size. There is no restriction on the number of circles used. Figures 18a, b, c, d, e, f, g, and h all represent the results of a more complex problem: students were asked to use two to four unit forms (circles) of the same shape and size to construct a superunit form, which is then repeated four times to make a design. Two levels of thinking are involved here. First, unit forms are not directly used to create the design but are grouped together to form superunit forms. Second, the superunit forms are used for the final design. The number of circles to be used in this problem should be no less than eight and no more than sixteen. The results of the first problem appear to be more pleasing because there are fewer

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CHAPTER 4: STRUCTURE

Most designs have a structure. Structure is to govern the positioning of forms in a design. Why is one group of unit forms displayed in a row and equidistant from one another? Why does another group of unit forms suggest a circular pattern? Structure is the underlying discipl~nefor such arrangements. Structure generally imposes order and predetermines internal relationships of forms in a design. We may have created a design without consciously thinking of structure, but structure is always present when there is organization. Structure can be formal, semi-formal, or informal. It can be active or inactive. It can also be visible or invisible. Formal Structure A formal structure consists of structural lines which are constructed in a rigid, mathematical manner. The structural l~nesare to guide the entire formation of the design. Space is divided into a number of subdivisions equally or rhythmically, and forms are organized with a strong sense of regularity. The various types of formal structure are repetition, gradation, and radiation. Repetition structures will be discussed later in this chapter. The other two types of formal structure will be dealt with in Chapters 6 and 7. Semi-formal Structure A semi-formal structure is usually quite regular, but slight irregularity exists. It may or may not consist of structural lines to

determine the arrangement of unit forms. Semi-formal structures will be discussed in Chapters 5, 8, and 10. Informal Structure An informal structure does not normally have structural lines. Organization is generally free and indefinite. We will come to this type of structure when we discuss contrast in Chapter 9. It will also be touched upon in Chapter 10. Inactive Structure All types of structure can be active or inactive. An inactive structure consists of structural lines which are purely conceptual. Such structural lines are constructed in a design to guide the placement of forms or unit forms, but they never interfere with their shapes nor divide the space up into distinct areas where color variations can be introduced. (Fig. 19a) Active Structure An active structure consists of structural lines which are also conceptual. However, the active structural lines can divide the space up into individual subdivisions which interact with unit forms they contain in various ways: (a) The structural subdivisions provide complete spatial independence for the unit forms. Each unit form exists in isolation, as if it had its own small frame of reference. It can have a ground of different color from that of its neighboring unit forms. Alternate, systematic, or random play of positive and negative forms can be introduced effectively. (Fig. 19b) (b) Within the structural subdivision, each unit form can move to assume various offcenter positions. It can even slide partially beyond the area defined by the structural

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subdivision. When this happens, the portion of the unit form that is outside the confines as clearly marked by the active structural lines may be cut off. Thus, the shape of the unit form is affected. (Fig. 19c) (c) When the unit form intrudes into the dominion of an adjacent structural subdivision, th~ssituation can be regarded as the encounter of two forms (the unit form and its adjacent structural subdivision), and interpenetration, union, subtraction, or intersection can take place as desired. (Fig. 19d) (d) Space isolated by a unit form in a structural subdivision can be united with any unit form or structural subdivision nearby. (Fig. 19e)

are considered as visible because they have a definite thickness which can be seen and measured. (Fig. 20b) Positive and negative visible structural lines can be used in combination in a design. For example, all horizontal structural lines can be positive, and all vertical structural lines negative. (Fig. 20c) Visible and invisible structural lines can also be used together. This means we can have only the verticals or the horizontals visible. Or visible and invisible structural lines can be used alternately or systematically, so that the visible structural lines mark off divisions, each of which actually contains more than one regular structural subdivision. (Fig. 20d)

Invisible Structure In most cases, structures are invisible, whether formal, semi-formal, informal, active, or inactive. In invisible structures, structural lines are conceptual, even though they may slice a piece off from a unit form. Such lines are active but not visible llnes of measurable thickness.

Repetition Structure When unit forms are positioned regularly, with an equal amount of space surrounding each of them, they may be said to be in a "repetition structure." A repetition structure is formal, and can be active or inactive, visible or invisible. In this type of structure, the entire area of the design (or a desired portion of it) is divided into structural subdivisions of exactly the same shape and size, without odd spatial gaps left between them. The repetition structure is the simplest of all structures. It is particularly useful in the construction of all-over patterns.

Visible Structure Sometimes a designer may prefer a visible structure. This means that the structural lines exist as actual and visible lines of desired thickness. Such lines should b e treated as a special kirid of unit form because they possess all the visible elements and can interact with the unit forms and the space contained by each of the structural subdivisions. (Fig. 20a) Visible structural lines can be positive or negative. When negative, they are united with negative space or negative unit forms, and they can cross over positive space or Positive unit forms. Negative structural lines

The Basic Grid The basic grid is the most frequently used in repetition structures. It consists of equally spaced vertical and horizontal lines crossing over each other, resulting in a number of square subdivisions of the same size. (Fig. 21) The basic grid provides each unit form the same amount of space above, below, left, and

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right. Except for the direction generated by the unit forms themselves, the vertical and horizontal directions are well-balanced, with no obvious dominance of one direction over the other.

Variations of the Basic Grid There are many other types of repetition structures, usually derived from the basic grid. Such variations of the basic grid are suggested as follows: (a) Change of proportion - The square subdivisions of the basic grid can be changed into rectangular ones. The balance of the vertical and the horizontal directions is thus transformed, and one direction gains greater emphasis. (Fig. 22a) (b) Change of direction - All the vertical or horizontal Ilnes, or both, can be tilted to any angle. Such diversion from the original vertical-horizontal stabil~tycan provoke a sense of movement. (Fig. 22b) (c) Sliding - Each row of structural subdivisions can slide in either direction regularly or irregularly. In this case, one subdivision may not be directly above or next to another subdivision in an adjacent row. (Fig. 22c) (d) Curving andlor bending - The entire set of vertical or horizontal Ilnes, or both, can be curved and/or bent regularly, resulting in structural subdivisions still of the same shape and size. (Fig. 22d) (e) Reflecting - A row of structural subdivisions as in (b) or (d) (provided that the twoouter edges of the row are still straight and Parallel to each other) can be reflected and repeated alternately or regularly. (Fig. 22e) (f) Combining - Structural subdivisions in a repetition structure can be combined to form bigger or perhaps more complex shapes. The new, bigger subdivisions

should, of course, be of the same shape and size, and fit together perfectly without gaps in the design. (Fig. 22f) (g) Further dividing - Structural subdivisions in a repetition structure can be further divided into small or perhaps more complex shapes. The new, smaller subdivisions should, again, be of the same shape and size. (Fig. 22g) (h) The triangular grid -Tilting of the direction of structural lines and further dividing the subdivisions thus formed, we can obtain a triangular grid. Three well-balanced directions are usually distinguished in this triangular grid, although one or two of the directions may appear to be more prominent. (Fig. 22h) (i) The hexagonal grid - Combining six adjacent spatial units of a triangular grid produces a hexagonal grid. It can be elongated, compressed, or distorted. (Fig. 22i) It is necessary to note that inactive (and invisible) structures should be rather simple, because the shape of the subdivisions remains unseen. Active (both visible or invisible) structures can be more complex. Since the shape of the subdivisions is to affect the design, care should be taken in relating them to the unit forms.

Multiple Repetition Structures When the structure consists of more than one kind of structural subdivisions which repeat both in shape and size, it is no longer a repetition structure but a "multiple repetition structure." A multiple repetition structure is still a formal structure. The various kinds (usually two, but there can be more) of structural subdivisions are woven together in a regular pattern. Examples of this type of structure are

mathematical semi-regular plane tessellations and structures consisting of repetitive shapes with regular gaps. (Fig. 23)

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Unit Forms and Structural S~~bdivisions In an inactive (and invisible) structure, unit forms are either positioned in the center of structural subdivisions, or at intersections of structural lines. They can fit exactly, be smaller or bigger than the subdivisions. If bigger, all adjacent unit forms will touch, overlap, interpenetrate, unite, subtract, or intersect one another. Sorneti~nesthey car1 be so big that one can cross over several others a simultaneously. In an active (visible or invisible) structure, each unit form is confined to its own spatial subdiv~sion,but it is not necessarrly placed right in the center of the subdiv~sion.It can lust fit, be smaller or bigger than the su bdivision, but it is seldom so big that it extends too much beyond the area of the subd~vision. Variations of position and direction can occur. Superunit forms are related to the structural subdrvisions in the same way, except that we may contain them in superstructural subdivisions which consist of several regular b subdivisions joined together. I

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Repetition of Position This has been mentioned in the preceding chapter. Repetition of position means that the unit forms are all positioned inside each subdivision in exactly the same way. In an inactive (and invisible) structure, there is always a repetition of position, because if the positioning of unit forms inside each subdivision varies, the regularil:~of the repetition structure may be easily destroyed. In an active (visible or invisible) structure, repetition of position is not always necessary.

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The active or visible structural lines provide sufficient discipline of repetition so that the freedom of positioning the unit forms, plus directional variations, may be fully explored.

Superimposition of Repetition Structures One repetition structure, along with the unit forms it carries, can be superimposed upon another repetition structure. The two structures and their unit forms can be the same or different from each other, Interaction of the two structures may produce unexpected results. (Fig. 24) Notes on the Exercises Figures 25a, b, c, d, e, and f exemplify the use of repetitive unit forms in an inactive (and invisible) repetition structure. The unit form here is a smaller circle enclosed by a bigger circle. The relationship of the smaller circle and the bigger circle has to remain consistent within each design. The use of active (and invisible) repetition structures is demonstrated in figures 26a, b, c, d, e, and f. The unit form here is similar to the one used in our problem for inactive repetition structure, except that the ring-like shape is broken, suggesting a form very much like the letter C. Comparing the results of the two problems, we should easily notice that straight lines are present in the designs with active structures but absent in those with inactive structures. The straight, active structural lines not only affecl the shape of unit forms and space surrounding them, but also change the nature of the design.

centers, the design may contain a distorted - By sliding the sectors of a centripetal center, or several hidden centers. (Fig. 49f) structure, the center of radiation can be (g) Gradual rotation of concentric opened up and a triangle, square, polygon, layers - If the concentric layers are not or star shape can be formed. (Fig. 50d) perfect circles but squares, polygons, or irregular shapes, they can be gradually Superimposition of Radiation Structures rotated. (Fig. 49g) As pointed out earlier, the three kinds of (h) Concentric layers with centrifugal radiation structure are interdependent. radiations - Centrifugal radiations can be Unless the unit forms are just the structural constructed within each concentric layer. lines themselves made visible, each kind of (Fig. 49h) radiation structure generally requires (i) Reorganized concentric layers another to produce fine structural The concentric layers can be reorganized so subdivisions for the accommodation of unit that some of the structural lines can be bent forms. (Fig. 51a) and linked with other structural lines, resultSuperimposition in this way is just a ing in interwoven patterns with one or more practical necessity. Which kind of radiation structure will dominate during this superimcenters. (Fig. 49i) position depends on the shape and posiThe Centripetal Structure tioning of the unit forms. In this kind of structure, sequences of bent Sometimes one radiation structure is suor curved structural lines press towards the perimposed upon another of the same type I center. The center is not where all the or a different type with a different purpose. The structural lines will converge but where all result is a complex composition, often proangles or curves formed by the structural ducing interesting moire patterns. (Fig. 51b) lines point towards. Radiation and Repetition (a) The basic centripetal structure This consists of equal sectors within each of A radiation structure may sometimes be which are constructed equidistant lines superimposed upon a repetition structure. parallel to the two straight sides of the secWith the repetition structure remaining tor, forming a series of angles progressing unchanged, the radiative structural lines towards the center. (Fig. 50a) may be shifted slightly so that the continuity (b) Directional change of structural lines of the radiative lines from one repetitive -The parallel lines in the basic centripetal strucstructural subdivision to the next is interrupted ture can change in direction, so that increas- to provoke a sense of movement. (Figs. 52a ingly acute or obtuse angles are formed at the and b) joining points of the structural lines. (Fig. 50b) A radiation structure may also be superim(c) Curving and bending of structural posed upon simple repetitive forms guided lines - The structural lines can be curved by an inactive repetition structure. (Fig. 52c or bent regularly, creating complex changes within the pattern. (Fig. 50c) Radiation and Gradation (d) Opening up of the center of radiation Most of the radiation structures illustrated

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earlier in this chapter are constructed with repetitive angles and/or spacing. However, gradational angles and/or spacing may be used in a great many of the cases. (Figs. 55f and g) A radiation structure may be superimposed on a gradation structure or a group of gradational unit forms in the same way as it is superimposed on a repetition structure or a group of repetitive forms. Structural Subdivisions and Unit Forms Structural subdivisions in a radiation structure are usually either repetitive or gradational, although they may also be similar to or plainly different from one another. In a centrifugal structure, the subdivisions are generally repetitive in both shape and size. Unit forms fit these subdivisions in the same way that they fit those in a repetition structure, except that the subdivisions normally carry the unit forms in their directional rotation. The unit forms may conform to the directions of the subdivisions or maintain a constant angle to the axis of each subdivision. (Figs. 53a and b) Within each of the subdivisions in a centrifugal structure, finer subdivisions can be constructed if desired. A sequence of parallel lines can be employed for the purpose, but there is virtually no limit to the ways of making further subdivisions. (Fig. 53c) In a regular concentric structure, the subdivisions are in the form of a ring which can only accommodate unit forms of a linear nature. A centrifugal structure is usually required for making fine subdivisions, and each ring can be rotated variably, if necessary, SO that the subdivisions in one ring do not have toalign with those in the next ring. (Fig. 53d) Subdivisions obtained in this way are

generally repetitive within each ring, but gradational from the center towards outer rings. Unit forms fit these subdivisions in the same way as they fit those in a gradation structure. Of course it is also possible to subdivide each concentric ring in a different manner if desired. (Fig. 53e) In a regular centripetal structure, the subdivisions are defined by sets of parallel lines which curl or bend towards the center. These can be further divided by superimposing sets of parallel lines, another centripetal structure, or a concentric structure. (Figs. 53f, g, h, and i) Unit Forms in Radiation We have spoken of unit forms in repetition, similarity, and gradation, and in each of these disciplines all the visual and relational elements can be considered. Radiation is a kind of discipline which involves structure only. If we have to speak of unit forms in radiation, it will be the concentric movement discussed under the heading of "Patterns of Gradation" in the chapter on gradation. Concentric movement creates a feeling of radiation, but basicallv it is a gradational use of unit forms. In planar rotation, the unit forms can be rotated in such a way that they all point to the physical center of the design. In planar progression, they can gradually move towards or away from the center from one concentric ring to the next. (Fig. 54a) Unit forms can be designed as miniature radiation patterns which are arranged repetitively or gradationally in a repetition structure. The effect is stdl very much like radiation. (Fig. 54b) Oversize Unit Forms A unit form can sometimes be almost as big

as the entire radiation pattern itself, or its length or breadth can be comparable to the diameter of radiation. Such oversize unit forms can be rotated along a centrifugal structure, maintaining a fixed relationship to each of the structural lines. During rotation, one unit form will inevitably cross over several or all other unit forms, and careful manipulation of overlapping, interpenetration, union, subtraction, and intersection will produce exciting results. (Fig. 54c) Irregular and Distorted Radiation Any irregular departure from regular radiation structures can be made if desired. Irregularity can occur only in one section of a regular pattern, but the entire design can be created with a vague center and loosely scattered radiating elements or series of irregular concentric rings. Photography and other mechanical means can be used to distort a regular radiation pattern. The pattern drawn or painted on paper can be photographed with a special lens, through a textured transparent screen or at an angle. It can also be curled, creased, folded, or crumpled, and then made into a flat picture by means of photography.

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Notes on the Exercises Figures 55a through n all illustrate radiation designs with unit forms more or less of a linear nature. In some examples the unit forms are just the structural lines made visible; in other examples they are designed to fit structural subdivisions. No attempt is made here to group the examples into the three kinds of radiation structure discussed in this chapter, because although some are immediately distinguish able as this or that kind, most are a blendin the different kinds. It is strongly suggested the examples should be carefully ana

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Visualization with Lines

Visllalization with Planes

A line is created by moving an appropriate tool across a surface by hand. It is easy to visualize a form constructed with lines. It is somewhat like drawing, except that solid lines of uniform breadth might be used in design creation. An outline is the most economical expression of basic visual information (fig. 20). If a fine line does not achieve the visual impact desired, a much bolder line could replace it (fig. 21). Within the outline details can be introduced that provide descriptive information and strengthen the connections and divisions of elements, the apparent volume and depth, and the spatial sequence from foreground to background of the form (fig. 22). A form can also be visualized with primary and secondary lines to clarify its structure; in this case. lines of two or more uniform breadths may be used (fig. 23).

The shape outlined in figure 20 can be painted black to create a continuous flat plane. The result is a silhouette-the simplest expression of a form (fig. 24). Black and white areas can be easily reversed; a black shape on a white background becomes a white, or negative, shape on a black background (fig. 25). A shape that is achieved with one continuous plane is usually void of details. Negative lines (white lines on the solid b!ack plane) can be used to introduce details. Negative lines separate a large plane into smaller planes (fig. 26).

Visualization with Points

Visualization with Texture

Repeated points can be arranged to outline a form (fig. 28). Points can also be grouped as a plane to suggest a form (fig. 29). When used to create planes, points produce texture.

Texture can be created with points, short lines, long lines, or any combination of these. Texture can be shown as a regular pattern, or as an irregular pattern, with slight variations in the shape or size of similar elements (figs. 30, 31). Texture generally adds visual variations to planes and surface characteristics to forms. Texture can also be applied in light-dark modulations to establish volume (fig. 32).

TYPES OF FORMS

Representational Forms

Forms can be broadly classified according to their particular contents. A form that contains a recognizable subject communicates with viewers in more than purely visual terms. This is called a representational form. When a form does not contain a recognizable subject, it is considered nonrepresentational or abstract.

A representational form can be rendered with photographic realism or with some degree of abstraction-as long as it is not so abstract as to make the subject unrecognizable (fig. 33). If the subject cannot be identified, the form is nonrepresentational. Sometimes the subject of a representational form is fantastic. The form, however, will present a transformed reality, one that suggests volume and space, so the fantastic subject conveys a kind of reality to the viewer (fig. 34).

Natural Forms

Man-made Forms

Representational forms can be further classified according to subject matter. If the subject is something found in nature, the form can be described as a natural form (fig. 35). Natural forms include living organisms and inanimate objects that exist on the earth's surface, in the oceans, or in the sky.

Man-made forms are representational forms that are derived from objects and environments created by man (fig. 36). They can feature buildings, furniture, vehicles, machines, tools, household products, toys, apparel, or stationery, to name a few possibilities.

Verbal Forms

Abstract Forms

Written language consists of characters, letters, words, and numerals t l ~ a make t precise visual communication possible. A form based on an element of written language is a a verbal form (fig. 37). A verbal form is representational in that it depicts a recognizable idea, rather than something that exists in a material sense.

An abstract form lacks a recognizable subject (fig. 38). It could be the designer's intention t o create a form that represents nothing. This form could have been based on a subject that has become obliterated after excessive transformation, or it could have been the result of experimentation with materials that led to unexpected results. An abstract form expresses a designer's sensitivity to shape, color, and composition without relying on recognizable elements.

TYPES OF SHAPES

Calligraphic Shapes

The same form, whether representational or abstract, can be expressed in different shapes. This does not mean that it must be seen from different views, angles, and distances, or that it rnust be moved or transformed; the different approaches possible in visual creation produce different resu Its. One approach is to draw the shape freehand in a somewhat calligraphic manner. Another approach is to create an organic shape by reducing a shape to all smooth curves. A third approach is to use only straight lines, circles, or arcs to establish a geometric shape.

The movement of the hand, the drawing tool, the medium, and the drawing surface are apparent in a calligraphic shape. The tool is generally a pen, pencil, or brush, whose particular characteristics are apparent in the finished form (fig. 39).

Organic Shapes

Geometric Shapes

The Multiplication of Planes

The same plane can be multiplied, or used repeatedly without change in shape or size. Each plane is thus seen as a component of a plural form. A plane that is multiplied can produce separate planes (fig. 134), ptanes that touch (fig. 135), planes that are joined (fig. 136), planes that overlap (figs. 137, 138), ptanes that interpenetrate (fig. 139), planes that combine positive and negative shapes (fig. 140).

The Multiplication of Planes

The same plane can be multiplied, or used repeatedly without change in shape or size. Each plane is thus seen as a component of a plural form. A plane that is multiplied can produce separate planes (fig. 134), planes that touch (fig. 135), planes that are joined (fig. 136), planes that overlap (figs. 137, 138), planes that interpenetrate (fig. 139), planes that combine positive and negative shapes (fig. 140).

The Division of Planes

A lane can be divided into equal or unequal parts. Negative lines can be

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introduced with gaps between dissected shapes (figs. 141, 142). The slight displacement of dissected shapes can lead to interesting effects, but the original shape of the plane must remain recognizable (fig. 143). Dissected shapes can touch, join, overlap, or interpenetrate (fig. 144).

Varying the Size of Planes

A plane can be enlarged gradually, or dilated. Smaller planes can then be placed within larger planes concentrically, or with slight variations in the direction or position of elements (figs. 145,146). Alternate positive and negative shapes might be overlapped (fig. 147).

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The Transformation of Planes

Planar shapes (or flat forms) can be rotated gradually to achieve transformation. The transformed shapes can then be superimposed (fig. 148). In addition, the size of shapes can be altered to suggest receding and advancing elements in space (fig. 149). As with size variations, alternate positive and negative shapes might be overlapped (fig. 150).

Folding Planes

Establishing Volume

A plane can be nianipulated to form a round or pointed corner where it is made to fold. Folding might expose the reverse side of a shape, which can then be visualized in outline (figs. 151, 152). A negative line can indicate a sharp fold (fig. 153).

A shape can be thickened along one or more of its edges to establish volume. The combination of lines and planes helps to distinguish the frontal plane from the side planes in a shape (figs. 154, 155). Volume can be presented with .the frontal plane turned obliquely or laterally (figs. 156, 157).

Regularity

Most geometric shapes are regular, or have components with consistent or orderly posi1:ions and directions. Shapes should be positioned at predetermined distances (fig. 158). The direction of shapes shot~ldbe at predetermined angles, establishing fan, circular, or spiral patterns (fig. 159). With two or four components, a sliape might resemble a square (fig. 160). With three components, a triangular shape might result (fig. 161).

Deviation

Symmetry

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Sometimes strict regularity produces a rigid composition, and some deviation is desirable. Deviation is effectively applied when one or more components change shape, size, position, or direction without seriously disrupting the original design (figs. 162-65).

Symmetrical shapes are regular shapes whose left and right halves are mirror images. An invisible straight line, an axis, divides the shape equally (fig. 166). A symmetricat shape can be positioned horizontally or on a slant (fig. 167).

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Slight deviation can be introduced in a svrnrnetrical shape by shifting the two halves out of alignment, by overlapping the halves, or by adding some variation to one of the halves (figs. 168-70).

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CREATING ORGANIC SHAPES

C and S Curves

Organic shapes are formed of smoott-lly flowing curves with imperceptible transitions or projecting connections. The curves are usually hand drawn, but drawing instruments, such as French curves or flexible curves, are sometimes used. Straight lines are rarely present. A shape created with curves and straight lines exhibits geometric as well as organic characteristics. Although simplicity is generally desirable, an organic shape can display intricate detai Is.

A line that flexes in a single direction results in a C curve (fig. 171). The other type of curve, an S cilrve, is produced when a line is flexed in two directions (fig. 172). Tlie S curve is actually two C curves joined from opposite directions. Both C and S curves can be presented as small or large loops (figs. 173, 174).

Shapes with Rounded Tips

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Two curves that meet can either establish a continuous flow or a pointed tip. Pointed tips can be seen either as projecting from the body of a shape (fig. 175), or as inverted toward it (fig. 177). Tips that are blunt (figs. 175, 177) can be sharpened by extending the curves near their junction (figs. 176, 178).

Any projecting or inverted tip can be rounded by smoothing the point (figs. 179, 180). This rounded tip can be exaggerated with a prominent ending (figs. 181, 182).

The Joining and Lir~kingof Shapes

The Splitting, Tearing, and Breaking of Shapes

Two shapes that overlap (fig. 183) can be partially joined (fig. 184). Two separate shapes (fig. 185) can be linked with protrusions (fig. 186).

A shape (fig. 187) can be split partially or conipletely into two or more shapes, while the overall image remains intact (figs. 188, 189). The split components might be marripulated to introduce slight variations if desired. The tearing and breaking of shapes result in ragged edges, which introduce some irregularity (fig. 190).

Cutting and Removing Parts of Shapes

The Curling and Twisting of Shapes

A portion, or portions, of a shape can be

A shape can be treated as a soft plane that c ~ ~ rto l sreveal the bottom or back of the shape (fig. 195). A shape can also be distorted by twisting it and narrowing its middle (fig. 196).

cut and removed, altering its edge (fig. 191), or producing negative shapes (figs. 192,193). Cut edges might be left ragged to suggest a forced break (fig. 194).

The Rippling and Creasing of Shapes

The Inflation and Deflation of Shapes

The excessive curling of a shape leads to ripples (fig. 197). Creases created by curling and rippling a shape can be given sharp edges (fig. 198). Creasing can be effected only halfway down the shape (fig. 199).

A shape can be inflated to considerable fullness (approaching a circle) without an obvious increase in size (fig. 200). It can also be deflated, or contracted, becoming crinkled, without an obvious decrease in size (figs. 201, 202).

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The Metamorphosis and Deformation of Shapes

The Proliferation of Shapes

A shape can metamorphose-be affected by internal growth in one or more specific areas (fig. 203). It can be deformed as if it is being acted upon by some external force that is squeezing, pulling. or pushing it (figs. 204-6).

Mul1:iple use of a shape is called proliferation (fig. 207). The size and shape of overlapped or superimposed, proliferated elements can vary (figs. 208-1 0).

Symmetrical Expression

Symmetry can be introduced in an organic shape. To achieve strict symmetry, a mirror image can be created of components on either side of an invisible axis (fig. 21 1). The axis, however, can become a C- or S-shaped curve, and the components can be appropriately adjusted for a symmetrical expression (fig. 212). Further manipulations of the resultant shape can a.lso be introduced (fig. 213). Components can vary slightly without destroying the symmetry of the structure (fig. 214).

VARIATIONS OF A FORM

A form, whether abstract or representational, geometric or organic, can be developed into different configuraations. The designer can thus examine all possible variations before deciding on one. Illustrations on the next few pages feature a variety of L-shaped forms (fig. 21 5).

Internal Variation

One way to change the shape of a form is to change the internal area from a solid plane (fig. 215 ) to an empty space. The form might have a fine or a bold outline (figs. 216, 217). The form call be split into two or more stripes (fig. 218), covered with a texture or pattern (fig. 2191, layered (fig. 220), or given other details (fig. 221).

External Variation

Extension

The two basic ways to vary a form externally are with corner (fig. 222) and edge variations (fig. 223). Sometimes internal variations lead to external variations, or vice versa. The combined external-internal variations can establish interesting results (figs. 224, 225).

A form can be extended with a border or concentric layers (fig. 226). Creating a frame of a certain shape (fig. 227), adding a shape to serve as background (fig. 2281, or introducing subsequent layers (Fig. 229) can also be used as extensions.

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Superimposition

Transfiguration

Other forms can be superimposed on a given form without obliterating its genera1 shape (figs. 230-32).

A form can be transfigured by changing a portion of the form or the entire form to something representational (figs.

233-35).

Dislocation

Distortion

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A form can be dissected or broken into two or more parts and then dislocated (figs. 236-38).

The simplest way to distort a form is to change the proportion of its height and width. This can be done by using a superimposed square grid as a guide (fig. 239). A grid of decreased height or narrower width is then drawn to map out a distorted shape (fig. 240). Diagonal distortion, circular distortion, or any other distortio~ican be effected in a similar manner (figs. 241, 242).

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A form can be regarded as a threedimensional plane that might bend, fold, or be seen froni different angles and distances (figs. 243-46). When 'thickness is added to a form, it acquires volume (fig. 247). It can be rotated in space, displaying a different shape (fig. 248). It can also be made to appear transparent (fig. 249). An extension to a form can approximate shadows or reflections cast on water (figs. 250-52).

Further Developments

All the previously me~itionedmethods of developing a form can be corn bined,

producing many more possible configurations (figs. 253-58).

253

255

FORMS AND SUBJECTS

Observing Natural Forms

Most representational forms capture the basic characteristics of shapes and avoid subjects with unusual, less familiar details. For instance, a leaf can be depicted as a shape representing leaves of most deciduous trees, or it can be depicted as a shape representing one particular tree. It is rare, however, that a leaf of an unusual shape is chosen as the subject for a design. Various ways of designing a form have been suggested in Part II, and these can be applied to the design of representational forms. It should first be decided whether to present a form as a geometric shape or as an organic shape, and how abstract it could be and still satisfy design goals. A preliminary search into a range of specimens is often desirable, so that their particularities can be compared and general features extracted. Drawing a selected specimen or two is necessary for achieving a thorough understanding of the subject.

Natural fornis are diverse, but possess the same basic structura.l characteristics determined by natural laws governing their growth. It is helpful to observe and identify the environmental forces that affect the shapes of natural forms. -The shapes of the components of natural forms and how they work together structurally should then be examined.

Spirals and Undulations

Linear shapes in nature are seldom linAcommon feature in .the structures of plants and animals is the existence of a ear in the geometric sense. These natural shapes actually curl slightly or backbone or central columnar shape with elements that branch bilaterally (fig. prominently in one or more directions. 259) or in an alternating pattern (fig. If a linear shape proceeds as a C 260). Branching can also take the form curve, winding around a center in graduof a splitting-one element splits into ated swirls, a spiral is formed (fig. 264). two, two into four, and so on (fig. 261). S~~ggesting three dimensions, a conical When more than two elements branch, (fig. 265) or tubular shape can be crea fanning pattern can result. Fanning ated (fig. 266). can extend 360 degrees, with rotating If it proceeds as an S curve, narrow or elements emerging from one central wide undulations result (figs. 267, 268). point (fig. 262), or surrounding a large Undulations can form a grooved shape or chain to suggest a third dimension open center (fig. 263). (figs. 269, 270).

Affinity and Unity

Observing Man-made Forms

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Elements within a particular natural form -cells, sections, or layers that make up a su rface-usual ly display affinity (figs. 271,272). These elements are not strict repetitions, but vary individually or progressively to conform to an overall shape and structure. There might be several types of elements, with affinity among elements of the different types. Affinity establishes unity. Unity is also established by fitting elements tightly together (fig. 273). Transitions create a smooth 'Tlow between elements (fig. 274).

Man-made forms are either crafted with tools by hand or nianufactured with machines. Generally, tools and machines are efficient at creating straight lines, Flat surfaces, right angles, circles, and cylinders. This explains why most man-made forms display a geometric configuration. Organic shapes are sometimes introduced as decorations, or for ergonomic reasons. The nature of its materials and the assembly of its parts are important considerations when observing a man-made form. It is also important to study the form from different viewpoints.

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Materials and the Assembly of Parts

Plans, Elevations, and Perspectives

Materials can be thin sheets or sol id masses, soft or hard, transparent or opaque, light or heavy. Materials used to fabricate man-made forms can be singular or can be parts that are assembled. Parts can be assem bled by fitting them, bonding them, or joining them with springs, pivots, or hinges, which allow for movement.

Man-made forms are often conceived as plans and elevations. Viewing the form from above establishes its plan (fig. 275). Viewing it from the front and sides establishes its elevations (figs. 276, 277). Plan and elevation studies are the basic ways of visualizing a man-made form. The form is then studied from different viewpoints, or perspectives (fig. 278). It must be noted that most planes are distorted when seen in perspective.

SELF-CONTAINED COMPOSITIONS

Establishing Singular Forms

Designing with representational forms can begin with a series of self-contained compositions-singu lar forms, plural d that are forms, and/or c o m p o ~ ~ nforms established without a frame of reference. These might then be contained within specific frames of reference to help define spatial relationships.

To create a singular form, the chosen subject is first studied from different viewpoints with drawings and sketches. One drawing (fig. 279) is then selected and used as the basis for design development. Consideration is given to aspects of aesthetics as well as communication. The singular form can be visualized as one solid plane (fig. 2801, planes displaying details (fig. 281), lines (fig. 283),the combination of lines and planes (figs. 282,284, 285), or a textured shape (fig. 286).

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Establishing Plural Forms

Repeating a singular form establishes a plural form (fig. 287). The singular forms, now components, could vary externally and/or internally (fig. 288). They could touch, overlap, join, or remain separate. Joining representational forms can result in a rather unnaturalistic, yet interesting design (fig. 289). Separate fornis must be adjacent, with one intruding the semienclosed space of the other if they are to be considered plural (fig. 290). Two or more components can be arranged in accordance with the following concepts: a. translation-varying the positions, but not the directions, of components (fig. . - 291) b. rotation-varyi ng the directions, with minimal change in position, of components (figs. 292-95) c. reflection-creating components as mirror images (figs. 296-98) d. dilation-increasing the size of superimposed or adjacent components (fig. 299) Positions of components are also effected with rotation and reflection and frequently with dilation. Positional changes in such cases should be kept to a minimum. C o m p o ~ ~ e ncan t s also be grouped randomly, or using a combination of the concepts desciibed above (figs. 300-306). L

288

I

Establishing Compound Forms

A compound form is established with dissimilar components, or with similar and dissimilar components. Used in a self-contained composition, a compound form can be taken as a singular form (figs. 307-9). Plural forms can be based on cornpound fornis, producing more intricate designs (figs. 310-1 4).

COMPOSITIONS WITH REPETITION

Two-way Continuance

Singular, plural, or compound forms can be applied as unit or superunit forms in repetition within a definite frame of reference. Their regular arrangement could establish a formal composition-all elements are organized in a kind of mathematical order. Repetition involves reproducing the same shape in a design as well as plating the shapes at intervals, which can be determined with lines forming an invisible structural grid.

The simplest composition with repetition involves the arrangement of unit or superunit forms as two-way continuance, resulting in rows that can extend vertically, horizontally, or at any given angle (figs. 315, 316). The row does not have to be straight. It can be crooked or curved. Unit forms can display a change of direction regularly within the row if desired.

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Four-way Continuance

When rows of unit or superunit forms are repeated regularly, four-way continuance is achieved (fig. 317). Conipositions with four-way continuance create a patternlike design (figs. 318-27). If a space is not completely filled, the coniposition becomes less formal (figs. 328, 329).

Six-way Continuance

A structural grid can comprise triangles to guide the placement of unit forms. This produces a six-way continuance, with shapes grouped as triangles or hexagons. If each unit form consists of a head and a tail, it is interesting to observe that the heads will meet at one point and the tails will meet at another point, in an alternating manner (figs. 330-34).

Development and Variations of the Repetition Structure

Unit forms can be photocopied (or traced) and cut out to explore all possible repetitions. A form can also be traced and then flipped over to obtain a mirror image (fig. 335). Superunit forms created this way can relate to each other in a different pattern of repetition, resulting in regular, but not monotonous, compositions (figs. 336-41). Isolated backgroundshapescanbechanged from white to black to achieve variations (figs. 342-44). The structural grid can can be made visible as actual lines of definite breadth, or made to become edges of spatial cells, embellishing the unit or superunit forms (figs. 345-47).

COMPOSITIONS WITH RADIATION

Full and Segmentary Radiation

'The repetition of unit or superunit forms around a common center results in radiation, which is a technique used in formal compositions. The basic structural grid for a design with radiation has a center of reference -the meeting point of all radiating lines, or the point around which structural lines revolve. Radiation normally features lines that converge near the tenter, with space between lines increasing as they move away from the center. Structural lines guide the placement of unit or superunit forms that are directly linked to or equidistant from the center of reference.

The 360-degree rotation of unit or superunit forms results in fult radiation. The center of reference could be the point at which lines converge, either exactly, overlapping, or at some regular distance from the center of reference. The angle of rotation for each form must be consistent to establish regularity (fig. 348). Rotating forms less than 360 degrees results in segmentary radiation (fig. 349). The fan or arc effect that results admits considerable background space near the center of radiation.

rn Rotation and Translation

A superunit form composed of translated unit forms can be rotated to achieve radiation (fig. 350). Rotated unit forms displaying radiation can be used as a superunit form for translation in a repetition structure (figs. 351 ,352).

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Rotation and Reflection

Rotation and Dilation

A full radiation might be cropped and joined to its mirror image on the other side of the cropped edge, which functions as an axis for reflection (fig. 353).

Dilated forms can be used instead of forms of uniform size. Slight variations of shape can be introduced during dilation if desired. These forms can be rotated to achieve a segmentary radiation, and then reflected or rotated again to achieve full radiation (figs. 354,355). Dilated forms in rotation can result in a spiral arrangement, a kind of radiation (fig. 356).

The Interception of Active Structural Lines

After establishing radiation, a composition could be superimposed with structural lines, making parallel or concentric subdivisions that intercept the forms. The interception could result in the dissection and partial dislocation of forms (figs. 357-61).

COMPOSITIONS WITH GRADATION

Gradation of Shape

Gradation refers to the systematic alteration of the shape, size, position, direction, or proportion of a form. The forms produced by these changes are then arranged in sequence, with smooth transitions between forms. Unit forms in gradation can be positioned according to a regular repetition structure with gradual variations. Unit forms can also be positioned with increasing or decreasing density.

Gradation of shape can be achieved by varying a form internally and/or externally. External without internal variation is achieved by adding to or subtracting from the form (fig. 362). Creating internal without external variations requires more prominent gradations. In most cases, shape gradations affect the external and internal aspects of a form (fig. 363). Any form can be changed to any other form with the appropriate number of shape gradations.

Gradation of Size

Gradation of Position

Size can be altered by enlarging or reducing forms arranged in sequence (usually in repetition). The transition could move from light to heavy rhythms, from heavy to light, or in an alternating fashion (fig. 364).

This is possible in a repetition structure with active structural lines that intercept and partially crop forms. The height of forms decreases as they are gradually moved down along the structural line (fig. 365).

Gradation of Direction

Rotating a form from left to right on a flat surface, while maintaining its shape, effects a change 1 i 1 direction (figs. 366, 367). It can also change direction if it is rotated from front to back in threedimensional space; different views are seen as different shapes (figs. 368, 369). Figure 370 features directional changes from left to right and from front to back, as well as gradations of shape and size.

COMPOSITIONS WITH SIMILARITY

If the shape, size, color, or texture of unit forms in a composition varies slightly, they are not part of a strict repetition, but are more loosely, or similarly, related. Similarity can also describe the placement of unit forms; the similar arrangement of unit forms might resemble a repetition, radiation, or a gradation structure.

Similarity and Repe,tition

Similarity and Radiation

The visual effect of close similarity is much like that of repetition. Similarity is achieved when a form is repeated with slight external and/or internal variations (figs. 374, 375). Forms in nature are never strict repetitions; no two leaves on the same tree are identical. Similarity can also be established by rotating a form and displaying different views (fig. 376). A formal structure can comprise similarly related forms that are not arranged in any sequence, introducing an element of informality to the design (figs. 377-79). A more informal design is achieved when the similarly related forms are distributed with similar density (fig. 380).

Rotated similar forms on a flat surface can be grouped regularly or freely to suggest radiation (figs. 381, 382).

Similarity and Gradation

COMPOSITIONS WITH CONCENTRATION

The arrangement of unit forms can proceed from dense to sparse in moderately smooth transitions to suggest gradation (fig. 383). Figure 384 illustrates this effect, but also features superimposed structural lines that intercept and crop the unit forms.

Concentration is the gathering of unit forms in particular areas of a composition. This establishes rhythmic movements, often creating a center of interest and subordinate accents. Concentration can be associated with natural phenomena-fleeting clouds, splashing water, falling leaves, migrating birds.

Points of Concentration

A point in a composition can mark the densest concentration of unit forms. Density could gradually give way to the sparse placement of elements; loose elements could activate otherwise blank space (figs. 385, 386). When there is more than one point of concentration, densities at the different points should vary, allowing one point to emerge as the center of interest. In dense areas, voids become prominent; a void is often the center of interest in a composition with tightly packed elements (fig. 387).

Linear Concentration

A concentrated area in a design can be linear, forming a band, with or without loose elements nearby (figs. 388-90). Unit forms within the band could vary in density (fig. 391). A composition could contain more than one band (fig. 392).

Planar Concentration

Unit forms can be brought together as a plane of almost even density. The plane could be an isolated shape within the frame of reference or could partially extend beyond it (fig. 393).

COMPOSlTlONS WITH CONTRAST

Contrast of Appearance

Contrast is used to suggest visual distinctions. Increased contrast enhances visibility. Decreased contrast assimilates elements in a composition. In most cases, contrast is used intuitively by the designer, but it can be consciously applied to effect comparisons and to establish a center of interest. Contrast can refer to the appearance, placement, or quantity of forms.

Contrast can be applied to one or more aspects of a form's appearance-its shape, size, color or texture. Contrasting shapes can differ externally or internally, or have different basic shapes (figs. 394,395). Contrast can be introduced by relating large and small forms (figs. 396-99). In a black-and-white design, a planar form and a linear form establish contrasting tones (figs. 400-402). Contrast of texture happens when some forms display fine details and others are plainly visualized forms (figs. 403-5).

Contrast of Placement

Contrast of placement refers to the position, direction, and spatial relationships of forms. Contrast of position refers to the arrangement of forms within the frame of reference (figs. 406, 407). Forms arranged in conflicting directions establish contrast (figs. 408, 409). Contrast of direction can also be achieved by rotating forms and presenting different views (fig. 410). Overlapping forms suggest depth (fig. 41 1). Forms of varying sizes suggest relative distances (fig. 412).

Contrast of Quantity

Contrast of quantity refers to the density and sparseness of elements in a composition when only one type of unit form is used (fig. 413). Contrast of quantity as mass and void can be arranged as fornis surrounding a blank area, or as fornis gatliered closely with a surrounding void (figs. 414, 415). If two types of unit forms are used, fewer instances of one forni car1 be contrasted with many instances of another (figs. 41 6-1 9).

COMPOSITIONS WITH ANOMALY

Anomaly in Shape

The combination of regular and irregular elements in a design establishes anomaly. Because regular elements are more numerous than irregular ones, anomaly also features contrasting quantities. Anomaly can be introduced only in formal compositions with a repetition, radiation, or a gradation structure. The strict regularity of the composition makes a slight irregularity prominent. Anomaly can be effected with the variation of shape, size, color, texture, position, or direction. An anomalous element usually marks the center of interest. Several anomalous elements can acccentuate different aspects of the design. Anomalous elements introduced too frequently lose their distinction as such and are seen as another set of unit forms.

The presence of a form different in shape from the unit forms introduces an anomaly. The shape can be completely different, or have only external andlor internal variations (figs. 420-22).

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Anomaly in Size

A particularly large or small form among unit forms of the same size introduces another type of anomaly. Fitting a large form into the composition might require the removal of some smaller unit forms (fig. 423).

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Anomaly in Color

Anomaly in Texture

One unit form can be changed from a planar shape to a linear shape to introduce anomaly in "color" to a black-andwhite design (fig. 424).

When one or more unit forms display texture or more details, anomaly in texture results (fig. 425).

1

Anomaly in Position and Direction

One or more unit forms can be dislocated in a composition, achieving anomaly in position and/or direction (figs. 426-28).

.fines the border of a plane, and marks the place where two planes join or intersect each other. (Fig. 9) (c) plane-the path of a line in motion (in a direction other than its own intrinsic direction) becomes a plane. A conceptual plane has length and breadth but no depth. It is bound by lines. It defines the external limits of a volume. (Fig. 10) (d) volume-the path of a plane in motion (in a direction other than its own intrinsic direction) becomes a volume. A conceptual volume has length, breadth, and depth, but no weight. It defines the amount of space contained or displaced by the volume. (Fig. 1 1 ) It is important to note that many of our three-dimensional ideas are first visualized on a flat piece of paper. We usually use a fine line to indicate the border of a plane or volume. This line is visual as it appears on the two-dimensional surface, but is conceptual when its only use is as a means of representing a three-dimensional form.

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Visual Elements Three-dimensional forms are seen differently from different angles and distances and under different lighting conditions. Therefore, we must consider the following visual elements to be independent of such variable situations: (a) shape-shape is the outward appearance of a design

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and the main identification of its type. A three-dimensional form can be rendered on a flat surface by multiple twodimensional shapes, and w e must be aware of this t o be able t o visually relate all such different aspects to the same form. (Fig. 12) (b) size-size is not just greatness or smallness, length or brevity, which can only be established by way of comparison. Size is also concrete measurement, and can be measured on any three-dimensional form in terms of length, breadth, and depth (or height, width, and thickness) from which its volume can be calculated. (Fig. 13) (c) color-color, or light and dark value, is what most clearly distinguishes a form from its environment, and it can be natural or artificial. When i t is natural, the original color of the material is presented. When it is artificial, the original color of the material is covered up by a coat of paint, or transformed by treating w i t h some other method. (Fig. 14) (d) texture-texture refers to the surface characteristics of the material used in the design. It may be naturally unadorned or specially treated. It may be smooth, rough, matt, or glossy as determined by the designer. It may be small-scale texture that accents twodimensional surface decoration or bolder texture that accents three-dimensional tactility. (Fig. 15)

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